The pair teamed up for new horror comedy The Menu, which is due to be released later this month.
As a huge Harry Potter fan, Taylor-Joy said it was a massive thing to be working with the man who played Voldemort in the films about the boy wizard.
But, opening up on The Graham Norton Show, the 26-year-old said she was able to squash down the excitement until they had wrapped.
She said: “I learnt English reading Harry Potter so it was a bit of a big deal but my subconscious does this thing of barring me from information that I can’t handle if I have a job to do, so I was cool and we got along really well.
"But the second it was over I like, ‘Oh my God!’ and rang my mum and said, ‘The last person that faced-off with Voldemort was Harry and now it’s me!’”
The Menu follows a young couple, played by Taylor-Joy and Nicholas Hoult, who travel to a remote island to eat at an exclusive restaurant that is run by talented but menacing celebrity chef Julian Slowik, who is played by Fiennes.
However, the food is treated like art, and contains some serious surprises.
Watch Anya Taylor-Joy and Ralph Fiennes in a clip from The Menu
Talking about the all the gourmet food in the movie, Taylor-Joy said: "I don’t eat much in the movie but I have to tip my hat to Nick Hoult who devoured everything each take.
"By take 37, I was like, ‘Dude, you are going to die!’”
The Menu is in cinemas from 18 November.
Watch: Anya Taylor-Joy craves 'life together' with partner Malcolm McRae